Mathematics for CSEC

Introduction
Preface
1 Number theory and computation
Whole numbers
Number bases and place value
Negative numbers
Order of operations
Properties of operations
Fractions
Powers and roots
Irrational numbers
Indices
Decimals
Approximations
Scientific notation
Converting fractions to decimals
Converting decimals to fractions
Percentages
Ratio
Division in a given ratio
2 Sets
Describing a set
Definitions and notation
Union and intersection
Venn diagrams
Harder problems
3 Algebra 1
Algebra
Definitions and conventions
Simplifying expressions
Factorising
Simplifying fractions
Substituting values into algebraic expressions
Linear equations in one unknown
Forming expressions and equations
Simultaneous linear equations in two unknowns
Linear inequalities
4 Measurement
Measurements
Units of measurement
Units of length
Units of mass
Units of time
Converting between units of measure
Temperature
Currencies
Speed
Imperial units
Units of length
Units of mass
Conversions between metric and imperial units
Polygons
Circles
Perimeter
Units of area
Areas of polygons and circles
Areas of irregularly shaped plane figures
Volume
Capacity
Prisms
Sources of error
5 Consumer arithmetic
Percentage increase and decrease
Compound percentage change
Reverse percentage problems
Profit and loss
Sales tax
Invoices and shopping bills
Utility bills and property tax
Hire purchase and mortgages
Salaries, wages and commission
Income tax
Investments and insurance
Review test 1
6 Relations, functions and graphs
Relations
Diagrams representing relations
Types of relation
Functions
Linear functions
Straight line graphs
The standard equation of a straight line
Parallel lines and perpendicular lines
The intercept form of the equation of a straight line
7 Geometry and trigonometry
Symmetry
Transformations
Describing a transformation
Parallel lines
Triangles
Quadrilaterals
Polygons
Necessary and sufficient conditions to prove that a quadrilateral is a parallelogram
Similar shapes
Congruent triangles
Pythagoras>' theorem
Bearings
Angles of elevation and depression
Trigonometry
Coordinate geometry
8 Statistics
Categorical and numerical data
Measures of central tendency
Frequency tables
Bar charts
Line graphs
Pie charts
Probability
Independent events
Mutually exclusive events
Contingency tables
9 Algebra 2
Binary operations
The product of two brackets
Factorising by grouping
Factorising quadratic expressions
Simplification of algebraic expressions
Quadratic equations
Solution by factorisation
Solution by completing the square
Solution by the formula
Changing the subject of a formula
10 Circle theorems
Definitions
Angles in circles
Cyclic quadrilaterals
Tangents to circles
Alternate segment theorem
Review test 2
11 Matrices
Definitions
Matrix multiplication
Determinants
The inverse of a matrix
Applications of matrices
Simultaneous equations
Numerical applications
12 Sequences
Sequences
13 Quadratic functions
The graph of a quadratic function
Estimation of the gradient at a point
Graphical solution of quadratic equations
Graphical solution of quadratic inequalities
Finding the maximum or minimum value of a quadratic function algebraically
Sketching the graphs of quadratic functions
Simultaneous equations DS one linear and the other quadratic
14 More functions
Cubic functions
The shape of a cubic curve
Reciprocal functions
Reciprocal curves
Recognising curves
Trigonometric functions
The graph of f(x) = sin x degrees
The graph of f(x) = cos x degrees
The sine and cosine functions
The tangent function
Growth curves
Decay curves
Exponential growth and decay
Vertical line test for a function
Inverse functions
The graph of a function and its inverse
Compound functions
Function of a function
15 Travel graphs
Straight line distanceDStime graphs
Rates of change
Tangents to curves
Travel graphs
Curved distanceDStime graphs
Velocity
Finding velocity from a distanceDStime graph
Velocity at an instant
Acceleration
VelocityDStime graphs
Finding the distance from a velocityDStime graph
Review test 3
16 Inequalities
Linear inequalities
Inequalities involving two variables
Shading the required region
Coordinates of points in a region
Greatest and least values
Linear programming
17 Variation
Formulae
Relationships
Direct variation
Dependent and independent variables
Inverse variation
Equations for inverse variation
18 Vectors in geometry
Definition of a vector
Representation of a vector
The magnitude of a vector
Equal vectors
Negative vectors
Multiplication of a vector by a scalar
Equivalent displacements
Addition of vectors
Subtraction of vectors
Position vectors
Vectors and geometry
Using vectors to model practical situations
Further problems
19 Transformations and matrices
The position vector of a point
The image of a position vector
Transformation matrix
Finding the image
Identifying a transformation
Reflections
Rotations
Enlargements
Transformations that cannot be described simply
Mixed transformations
The identity transformation
Transformations and images
Inverse transformations
Inverse matrix transformations
Inverse matrices and inverse transformations
An invariant point
Transformations not using matrices
20 Compound transformations
Compound transformations
Equivalent single transformations
The identity transformation
Common transformation matrices
Area scale factor
Unit vectors and the unit square
Finding a transformation matrix
Compound transformations
Defining transformations as matrix equations
Compound transformations and matrices
Review test 4
21 Sine and cosine formulae
Sines of obtuse angles
Cosines of obtuse angles
Trigonometric ratios as fractions
Trigonometric ratios of 30 degrees, 45 degrees and 60 degrees
Triangle notation
The sine rule
Using the sine rule to find an angle
The cosine rule
Mixed questions
The area of a triangle
Sine formula for area of a triangle
Heron>'s formula
The area of a segment of a circle
Applications
22 Constructions and transformations
Constructions using ruler and compasses
Accuracy
Scales
Transformations
Finding the mirror line
Finding the centre of rotation
Circles and tangents
Parallel lines
23 Grouped data
Collecting information
Frequency tables
Class intervals
Measures of central tendency of a grouped frequency distribution
The modal group
The group containing the median
The mean
Histograms
Frequency polygons
Using the area under a histogram
24 Measures of spread
Range
Cumulative frequency tables
Cumulative frequency curves
Drawing a cumulative frequency curve
Quartiles
Statistical investigations
Deciding which statistical measure to use
25 Areas and volumes
Pyramids
Volume of a pyramid
Surface area of a pyramid
Volume of a cylinder
Curved surface area of a cylinder
Volume of a cone
Surface area of a cone
Volume of a sphere
Surface area of a sphere
Review test 5
Multiple choice tests
Model exams
Sample paper with solutions
Answers
Index